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Question

If sin2α=4sin2β, then 5tan(αβ)tan(α+β)= is

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Solution

sin2α=4sin2β
5tan(αβ)tan(α+β)=5sin(αβ)cos(α+β)sin(α+β)cos(αβ)
=5(2sin(αβ)cos(α+β)2sin(α+β)cos(αβ))
=5(sin2αsin2βsin2α+sin2β)
=5(3sin2β5sin2β)
5tan(αβ)tan(α+β)=3

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